I don't think there's a difference. For instance, let's say we have a video of little Timmy shoplifting a candy bar. Clear face shot, maybe the video even has sound and there's a vocal-print match. Pretty slam-dunk case, right? Not much room for reasonable doubt there.

Oh, but you see, little Timmy was actually being telepathically controlled by a diabetic alien about to pass out from hypoglycemia, who had him steal the candy bar. Can you prove this was not the case?

This is what reasonable doubt protects against. There will always be the ability to create a (probably fanciful) scenario in which the defendant is not guilty. An unreasonable scenario, one might even say. Being able to convince the jury beyond reasonable doubt is as close to 100% proof as you are reasonably going to ever get.

> Beyond "the shadow of a doubt" is sometimes used interchangeably with beyond reasonable doubt, but this extends beyond the latter, to the extent that it may be considered an impossible standard. The term "reasonable doubt" is therefore used. [Emphasis mine]